Lemma 1 
([1]}, Hermitian construction) A Hermitian dual-containing \([n, k]_{q^{2}}\)  linear code \(\mathcal {C}\)  such that there are no vectors of weight less than \(d\)  in \(\mathcal {C} \backslash C^{\perp _{h}}\)  yields a pure QECC with parameters \([[n, 2 k-n, d]]_{q}\) .

